S5_Unit_1_Outcome_1

# S5_Unit_1_Outcome_1 - www.mathsrevision.com Higher Outcome 1

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Unformatted text preview: www.mathsrevision.com Higher Outcome 1 www.mathsrevision.com www.mathsrevision.com Higher Unit 1 Higher Unit 1 Distance Formula The Midpoint Formula Gradients Collinearity Gradients of Perpendicular Lines The Equation of a Straight Line Median, Altitude &amp; Perpendicular Bisector Concurrency Exam Type Questions www.mathsrevision.com Higher Outcome 1 Distance Formula Distance Formula Length of a straight line Length of a straight line A(x 1 ,y 1 ) B(x 2, y 2 ) x 2 x 1 y 2 y 1 C x y O This is just Pythagoras Theorem 2 2 2 (AB) =(AC) +(BC) www.mathsrevision.com Higher Outcome 1 Distance Formula Distance Formula The length (distance ) of ANY line can be given by the formula : 2 2 2 1 2 1 tan ( ) ( ) d is c e AB y y x x =- +- Just Pythagoras Theorem in disguise www.mathsrevision.com Higher Outcome 1 =- +- 2 2 2 1 2 1 tan ( ) ( ) d is c e AB y y x x www.mathsrevision.com Higher Outcome 1 Collinearity Collinearity A C x y O x 1 x 2 B Points are said to be collinear if they lie on the same straight. The coordinates A,B C are collinear since they lie on the same straight line. D,E,F are not collinear they do not lie on the same straight line. D E F www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory www.mathsrevision.com Higher Outcome 1 Finding Mid-Point of a line Finding Mid-Point of a line A(x 1 ,y 1 ) B(x 2, y 2 ) x y O 1 2 1 2 , , 2 2 y y x x M + + = x 1 x 2 M y 1 y 2 The mid-point ( Median ) between 2 points is given by Simply add both x coordinates together and divide by 2. Then do the same with the y coordinates. www.mathsrevision.com Higher Outcome 1 1 2 1 2 , , 2 2 y y x x M + + = www.mathsrevision.com Higher Outcome 1 Straight line Facts Straight line Facts Y axis Intercept 2 1 2 1 y - y Gr ad ie nt = x - x y = m x + c Another version of the straight line general formula is: ax + by + c = 0 www.mathsrevision.com Higher Outcome 1 Feb 13, 2012 www.mathsrevision.com 10 m &lt; 0 m &gt; 0 m = 0 x = a y = c Sloping left to right up has +ve gradient Sloping left to right down has -ve gradient Horizontal line has zero gradient. Vertical line has undefined gradient. www.mathsrevision.com Higher Outcome 1 Feb 13, 2012 www.mathsrevision.com 11 m = tan m &gt; 0 Lines with the same gradient means lines are Parallel The gradient of a line is ALWAYS equal to the tangent of the angle made with the line and the positive x-axis www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory 60 o 60 o www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory www.mathsrevision.com Higher Outcome 1 Straight Line Theory Straight Line Theory www.mathsrevision.comwww....
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## S5_Unit_1_Outcome_1 - www.mathsrevision.com Higher Outcome 1

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